Question

Which of the following functions has a graph that is a line?

Answer 1

Right answer:

f(x)=x

In geometry, a line is straight (no curves) and has no thickness,. This extends in both directions without end, that is, infinitely. We need to find from the options the graph of a line, recall that a function $f$ from a set $A$ to a set $B$ is a relation that assigns to each element $x$ in the set $A$ exactly one element $y$ in the set $B$. The set $A$ is the domain (also called the set of inputs) of the function and the set $B$ contains the range (also called the set of outputs).

Therefore, the right option is $f(x)=x$ as illustrated in the Figure below.

Answer 2

Answer:

f(x) =x

Step-by-step explanation:

Given are three functions of x

We have to find the function whose graph is a straight line

We know that a straight line has constant slope throughout its domain

Let us check with this

I function

$f(x) =x$

Differentiate to find the slope

Slope =1 = constant

Hence this is a straight line

2 function

$f(x) = x^ 2\\f'(x) =2x$

Thus slope depends on the value of x and not a constant.  This cannot be a straight line

3 function

$f(x) =|x|\\i.e. f(x) = -x, x$

This function has slope 1 for positive x and -1 for negative x

Since not constant cannot be a straight line

So answer is option A